Access a property in python from a menu
Instead of adding a layout.operator you would add a layout.prop, which would look like this:

self.layout.prop(context.scene.tool_settings, "use_mesh_automerge")


The first parameter in the parentheses is where the property is stored and the second is the name of the property you wish to access.

This results in this menu, with a property that can be toggled on and off: